Which of the following numbers is a factor of 175? ${5,8,9,11,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $175$ by each of our answer choices. $175 \div 5 = 35$ $175 \div 8 = 21\text{ R }7$ $175 \div 9 = 19\text{ R }4$ $175 \div 11 = 15\text{ R }10$ $175 \div 14 = 12\text{ R }7$ The only answer choice that divides into $175$ with no remainder is $5$ $ 35$ $5$ $175$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $175$ $175 = 5\times5\times7 5 = 5$ Therefore the only factor of $175$ out of our choices is $5$. We can say that $175$ is divisible by $5$.